By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]Hello, I need help completing this math problem. I will include a picture. Thank you so much!
From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,
[tex]5^2+8^2=x^2[/tex]where x denotes the missing length. Then, our equation give us
[tex]\begin{gathered} x^2=25+64 \\ x^2=89 \end{gathered}[/tex]By taking square root to both side, we have
[tex]\begin{gathered} x=\sqrt[]{89} \\ x=9.4339 \end{gathered}[/tex]Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft
4(px+1)=64The value of x when p is -5 is ?
Answer:
x = -3
Explanation:
Given the equation:
[tex]4\left(px+1\right)=64[/tex]We are required to find the value of x when p is -5.
[tex]\begin{gathered} 4\left(px+1\right)=64\colon p=-5 \\ 4\left(-5x+1\right)=64 \\ -20x+4=64 \\ -20x=64-4 \\ -20x=60 \\ \text{Divide both sides by -20} \\ x=\frac{60}{-20} \\ x=-3 \end{gathered}[/tex]The distance to the nearest exit door is less than 200 feet.
ANSWER
d < 200
EXPLANATION
If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.
how many ones equal 4 tens
We have to find the number of ones in 4 tens.
As we know that, there are 10 ones in a 10.
Therefore, in 4 tens, the total number of ones would be 1 x 4 x 10 = 40
7.5 is 15% of what number?
Let the number be x. So equation for x is,
[tex]\begin{gathered} \frac{15}{100}\cdot x=7.5 \\ x=\frac{7.5\cdot100}{15} \\ =\frac{750}{15} \\ =50 \end{gathered}[/tex]The number is 50.
Use the Distibutive Property: Expand -3(x + 3)
The distributive property of multiplication states the following:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, for the given expression, we have:
[tex]-3(x+3)=(-3)\cdot x+(-3)\cdot3=-3x-9[/tex]You randomly draw a marble from a bag of marbles that contains 7 blue marbles 2 green marbles and 1 red marbles
Given the following:
7 blue marbles
2 green marbles
1 red marbles
We to find the probability of not drawing a blue marble.
We will be solving it in two ways.
First let's get the total marbles
Total Marble = 7 + 2 + 1 = 10
recall that probablity is number of favourable outcome divide by number of total outcome.
So,
probablity of Drawing a Blue Marble is = 7/10
probability of not Drawing Blue Marbles = 1 - Probability of Drawing Blue Marbles
= 1 - 7/10
= 10 - 7
10
= 3/10
OR
Probability of not Drawing Blue Marbles = Probablity of drawing Green or Red Marbles.
= 2/10 + 1/10
= 3/10
Therefore, the probability of not Drawing Blue Marbles is 3/10.
v+1.6>-5.5
nnnnnnnnnnnn
Answer:
v > -7.1
Step-by-step explanation:
Find the interest odf the loan using banker's ruleP - $350,- = 4.8%, t = 150 days
i = P r T
interest: i
Principal = $350
Interest rate : 4.8% (in decimal form, 4.8/100 = 0.048)
time = t = days/365 = 150/360
Replacing:
i= 350 (0.048) (150/360) = 7
Give the first four terms of the geometric sequence for which A1 = -7 and r = -4.07 7 7 74, 16, 64, 256 -7,28, -112, 448 -7, -11, -15, -1928. -112, 448. - 1792
Given:
[tex]\begin{gathered} firstterm(a_1\text{) = -7} \\ \text{common ratio (r) = -4} \end{gathered}[/tex]Required: First four terms
The nth term of a geometric sequence :
[tex]a_{n\text{ }}=a_1\text{ }\times r^{n-1}[/tex]Hence, we can obtain the next four terms by substituting
[tex]\begin{gathered} \text{when n = 1, a}_1\text{ = -7} \\ n=2,a_2\text{ =-7 }\times(-4)^{2\text{ - 1}} \\ a_2\text{ = -7 }\times\text{ -4} \\ =\text{ 28} \\ \\ \text{when n =3, a}_3\text{ = -7 }\times(-4)^{3\text{ -1 }} \\ a_3\text{ = -7 }\times\text{ 16} \\ =\text{ -112} \\ \\ \text{when n = 4, a}_4\text{ = }-7\text{ }\times(-4)^{4-1} \\ a_4\text{ = -7 }\times\text{ -64} \\ =\text{ 448} \end{gathered}[/tex]Michael earns (2x3 + 3x) every month. His wife earns (3x2 + 6) every month. x represents the number of days they work in a month. What is the total earnings in a month?2x3 - 3x2 + 3x - 62x3 + 3x2 + 3x + 66x5 + 21x3 + 18x(2x3 + 3x) / (3x2 + 6)
From the question, we can derive the following:
Micheal earns 2x³ + 3x
His wife earns 3x² + 6
If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.
So we will have:
(2x³ + 3x) + (3x² + 6)
Adding up the two earnings:
2x³ + 3x² + 3x + 6
So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.
So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).
which of the following liner equations passes through points (-1,5) and (1,5)?
Hence, the correct option is Option D. None of the choices are correct.
Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
The probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is .
in the question ,
it is given that
the waiting time is randomly distributed between 0 and 6 minutes .
Since it is uniformly distributed , the Uniform distribution have two bounds a and b .
The probability of finding the value greater than x can be calculated using the formula .
P(X>x) = (b-x)/(b-a)
Given that , the waiting time is Uniformly distributed 0 and 6 minutes , we get a=0 and b=6,
Substituting the values in the Probability formula , we get
P(X>2.25) = (6-2.25)/(6-0)
= 3.75/6
= 0.625
Therefore , the probability that a randomly selected passenger have a waiting time greater than 2.25 minutes is 0.625.
The given question is incomplete , the complete question is
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes.
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Find the lateral surface area and volume of the object in picture below
So first of all we have to find the lateral surface of the truncated pyramid. This surface is composed of 4 equal trapezoids. The are of a trapezoid is given by half the sum of its bases multiplied by its height. The large base of these faces are 6' long, the short base are 5' long and their height are 2.1' long. Then the area of each trapezoid is:
[tex]\frac{(6^{\prime}+5^{\prime})}{2}\cdot2.1^{\prime}=11.55in^2[/tex]Then the total lateral surface is:
[tex]11.55in^2\cdot4=46.2in^2[/tex]Then we need to find the volume of the truncated pyramid. This is given by the following formula:
[tex]\frac{1}{3}h(a^2+ab+b^2)[/tex]Where a and b are the bottom and top side of its two square faces and h is the height of the pyramid i.e. the vertical distance between bases. The lengths of the bases is 5' and 6' whereas the height of the pyramid is 2' then its volume is given by:
[tex]\frac{1}{3}\cdot2^{\prime}\cdot(5^{\prime2}+6^{\prime}\cdot5^{\prime}+6^{\prime2})=60.7in^3[/tex]In summary, the lateral surface is 46.2in² and the volume is 60.7in³.
David had $350. After shopping, he was left with $235. If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.(Not sure if I'm expressing this correctly.)c = amount spent350 - c = 235c= 115
Given:
David had $350. After shopping, he was left with $235.
Required:
If c represents the amount he spent, write an equation to represent this situation. Then use the equation to find the amount of money David spent.
Explanation:
We know c is the amount spent
So,
Available amount = Total amount - spent amount
235 = 350 - c
c= 350 - 235
c = 115
Answer:
Hence, David spent $115.
A plane intersects both bases of a cylinder, passing through the center of each baseof the cylinder. What geometric figure will be formed from this intersection?
When a plane intersects both bases of a cylinder, passing through the center of each base of the cylinder, the cross section formed is a rectangle.
New York City is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 2 vans and 6 buses with 244 students. High School B rented and filled 4 vans
and 7 buses with 298 students. Every van had the same number of students in it as did the buses.
Find the number of students in each van and in each bus.
There are eight students in each van and 38 students are in each bus.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
Let the number of students fit into a van would be v
And the number of students fit into a bus would be b
School A:
2v + 6b = 244 ...(i)
2v = 244 - 6b
v = 122 - 3b
School B:
4v + 7b = 298 ...(ii)
Substitute the value of v = 122 - 3b in the equation (ii),
4(122 - 3b) + 7b = 298
Solve for b to get b = 38.
Substitute the value of b = 38 in equation (i),
2v + 6(38) = 244
2v + 228 = 244
2v = 16
v = 8
Therefore, eight students are in each van and 38 students are in each bus.
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Given the measure -845°, which answer choice correctly gives an angle measure coterminal with the given angle and on the interval,0 < 0 < 360
Given the measure -845° we can find its coterminal measure on the interval, [0,360) below
Explanation
For angles measured in degrees
[tex]\begin{gathered} β=α±360*k,where\text{ }k\text{ }is\text{ }a\text{ }positive\text{ }integer \\ -845°=\frac{-169}{36}π≈-4.694π \\ Coterminal\text{ }angle\text{ }in\text{ \lbrack}0,360°)range:\text{ 235\degree, located in the third quadrant.} \end{gathered}[/tex]Answer: Option A
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
Write a multiplication expression to represent each situation. Then find each product and explain its meaning. Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week.
We know that
• Ethan burns 650 calories per hour.
If he runs 5 hours we just have to multiply this time with the given rate.
[tex]650\cdot5=3,250[/tex]Therefore, Ethan burns 3,250 calories in 5 hours.Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]find the slope of the line that passes through (10,2) and (2,10)
Suppose that $2000 is invested at a rate of 2.8%, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.Do not round any intermediate computations, and round your answer to the nearest cent.
Solution:
Given the amount invested, P; the rate, r, at which it was invested and the time, t, it was invested.
Thus,
[tex]\begin{gathered} p=2000, \\ \\ r=2.8\text{ \%}=0.028 \\ \\ t=5 \end{gathered}[/tex]Then, we would solve for the total amount, A, using the formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ Where; \\ n=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} A=2000(1+\frac{0.028}{4})^{(4)(5)} \\ \\ A=2000(1.007)^{20} \\ \\ A=2299.43 \end{gathered}[/tex]ANSWER: $2,299.43
Tasty Subs acquired a food-service truck on October 1, 2024, for $23,100. The company estimates a residual value of $1,500 and a six-year service life. Required:Calculate depreciation expense using the straight-line method for 2024 and 2025, assuming a December 31 year-end.
The company estimates a residual value of $1,500 and a six-year service life.
It is given that,
Cost of truck delivery = $ 23100
Salvage value = $ 1500
Useful life = 6 years
Depreciation expenses by using the straight-line method are calculated as,
[tex]Depreciation\text{ expenses p.a = }\frac{cost\text{ - salvage value }}{useful\text{ life}}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} Depreciation\text{ expenses p.a = }\frac{23100\text{ - 1500}}{6} \\ Depreciation\text{ expenses p.a = }\frac{21600}{6} \\ Depreciation\text{ expenses p.a = 3600} \end{gathered}[/tex]Thu
What is 58 divided into 7275
Answer:125.431034
Step-by-step explanation:
In ΔVWX, m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2. Find m∠W.
The measure of angle W in the triangle is 29 degrees
How to determine the measure of angle W?The definition of the angles are given as
m∠V=(6x−4, m∠W=(x+12), and m∠X=(3x+2)
Where the triangle is given as
Triangle VWX
The sum of angles in a triangle is 180 degrees
This means that
V + W + X = 180
Substitute the known values in the above equation
So, we have
6x - 4 + x + 12 + 3x + 2 = 180
Evaluate the like terms
10x = 170
Divide by 10
x = 17
Substitute x = 17 in m∠W=(x+12)
So, we have
m∠W=(17+12)
Evaluate
m∠W = 29
Hence, the angle W is 29 degrees
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The change in the value of a stock is represented by the rational number -5.90 describe in words what this means
The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.
Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.
On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.
For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.
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A bakery makes and sells hot cocoa bombs during the holidays. The first 12 hot cocoa bombs of an order cost is $4.00 each. Each of the next 6 hot cocoa bombs cost $3.50 each. For orders exceeding 18, the cost drops to $3 each. The function C(x) represents the bakery's pricing.
Solution
Step 1
Given data for C(x), the bakery's pricing
[tex]\begin{gathered} F\text{or this range 0}\leq x\leq12ofhotcocoabombs\text{ we use C(x) =4x} \\ \text{For this range }1218,ofhotcocoabombs\text{ we useC(x) = }3x+15 \end{gathered}[/tex]Required
Step 1
To find the cost of 8 hot cocoa bombs
[tex]\begin{gathered} C(8)\text{ lies in the range 0}\leq x\leq12 \\ \text{Hence we use 4x where x = 8} \\ \text{The cost of 8 hot cocoa bombs = 4(8) = \$32} \end{gathered}[/tex]Step 2
To find the cost of 18 hot cocoa bombs
[tex]\begin{gathered} C(18)\text{ lies in the range 12}Step 3To find the C(30)
[tex]\begin{gathered} C(30)\text{ lies in the range x}\ge18 \\ \text{Hence we use 3x +15, where x = 30} \\ C(30)\text{ = 3(30) + 15 = 90 + 15 = \$105} \\ \end{gathered}[/tex]Step 4
What C(30) represents.
C(30) represents the cost of ordering 30 hot cocoa bombs which is $105
Dilate trianglesDraw the image of AABC under a dilation whose center is A and scale factor is
Since the dilation is centered at vertex A, the coordinates of A' are the same of A.
Then, to find the coordinates of B, let's multiply the distance AB by the scale factor:
[tex]\begin{gathered} AB=12.6\\ \\ A^{\prime}B^{\prime}=12.6\cdot\frac{1}{4}=3.15 \end{gathered}[/tex]Doing the same for AC, we have:
[tex]A^{\prime}C^{\prime}=AC\cdot\frac{1}{4}=11.3\cdot\frac{1}{4}=2.825[/tex]The points B' and C' are on the sides AB and AC, respectively.
Knowing this, let's draw the image A'B'C':
Since AB = BC, we also have A'B' = B'C' = 3.15.
Leila triples her recipe that calls for 2/5 of a cup of flour. Leila has 1 cup of flour. Does she have enough to triple her recipe?
no
yes
Answer:
No
Step-by-step explanation:
3 × [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex] cups required to triple her recipe
she only has 1 cup
so does not have enough to triple her recipe
Answer:
No
Step-by-step explanation:
If she triples it that means you need to triple the 2/5 so she would neew 6/5 of flour which is 1/5 more than what she has.